To practice solving a compound inequality connected by 'or', evaluate $1 - 2x \leq -3$ or $7 + 3x \leq 4$. For the first inequality, subtracting $1$ yields $-2x \leq -4$, and dividing by $-2$ (reversing the inequality sign) gives $x \geq 2$. For the second inequality, subtracting $7$ yields $3x \leq -3$, and dividing by $3$ gives $x \leq -1$. Graphing both results shows that the union consists of two distinct regions: numbers less than or equal to $-1$ and numbers greater than or equal to $2$. In interval notation, this combined solution is written as $(-\infty, -1] \cup [2, \infty)$.